Sine Plate Calculator
Calculate the gauge block height needed to set a sine plate to any angle, or find the angle from a known stack height. Sine plates offer a wider, clamped surface than sine bars \u2014 ideal for grinding and milling setups.
Gage Block Height
5.0000 in
= 127.0000 mm
Quick reference \u2014 Gage block heights (inches)
| Angle | 5″ plate | 10″ plate |
|---|---|---|
| 5\u00b0 | 0.4358 | 0.8716 |
| 10\u00b0 | 0.8682 | 1.7365 |
| 15\u00b0 | 1.2941 | 2.5882 |
| 20\u00b0 | 1.7101 | 3.4202 |
| 25\u00b0 | 2.1131 | 4.2262 |
| 30\u00b0 | 2.5000 | 5.0000 |
| 35\u00b0 | 2.8679 | 5.7358 |
| 40\u00b0 | 3.2139 | 6.4279 |
| 45\u00b0 | 3.5355 | 7.0711 |
| 50\u00b0 | 3.8302 | 7.6604 |
| 55\u00b0 | 4.0958 | 8.1915 |
| 60\u00b0 | 4.3301 | 8.6603 |
How a sine plate works
A sine plate uses the same trigonometric principle as a sine bar: sin(\u03b8) = opposite / hypotenuse. The plate length between roller centers is the hypotenuse; the gauge block stack is the opposite side.
Sine plates are preferred over sine bars when you need to clamp workpieces securely, work with heavier parts, or set angles above 45\u00b0.
When to use a sine plate
Surface grinding
Clamp workpieces at precise angles for angular grinding operations on surface grinders.
Heavy workpieces
The wide platform and clamps handle parts too heavy or bulky for a narrow sine bar.
Angles above 45°
Sine plates are more stable at steeper angles than sine bars, reliable up to ∼60°.
Compound angles
Compound sine plates set angles in two planes simultaneously for complex machining.
Milling fixturing
Tilt workpieces for angular milling when a rotary table or tilting vise is unavailable.
Quality inspection
Verify machined angles on production parts with gauge-block precision.
Frequently asked questions
What is a sine plate?
A sine plate is a precision metrology fixture with a wide, flat clamping surface and two ground cylinders at a fixed distance apart. Unlike a narrow sine bar, the plate provides a stable platform for clamping larger or heavier workpieces, making it ideal for surface grinding and milling setups.
How is a sine plate different from a sine bar?
Both use the same trigonometry (Height = Length × sin(Angle)), but a sine plate has a wider surface with built-in clamps or T-slots. Sine plates are preferred for heavy workpieces, angles above 45°, and setups requiring secure clamping. Sine bars are lighter and used for inspection tasks.
What angles can a sine plate handle?
Sine plates can reliably set angles from 0° to about 60°. Above 60°, accuracy decreases. Some compound sine plates allow angles in two planes simultaneously. For very steep angles, a sine vise or tilting fixture may be more practical.
What is a compound sine plate?
A compound sine plate has two stacked plates oriented 90° to each other, allowing you to set angles in two planes simultaneously. Each plate uses its own gauge block stack. This is essential for machining compound angles on parts like turbine blades.
How do I calculate gauge block height?
Use the formula: Height = Plate Length × sin(Angle). For a 10-inch plate at 30°: Height = 10 × sin(30°) = 10 × 0.5 = 5.0000 inches.
What are common sine plate sizes?
Common sine plate lengths include 5", 10", and 12" (imperial) and 100 mm, 200 mm, and 300 mm (metric). Larger plates (12"+ or 300 mm+) are used for heavy-duty grinding and milling operations.
Can I use metric gauge blocks with an imperial sine plate?
Technically yes, but it adds unnecessary complexity. Use gauge blocks matching your plate’s unit system. This calculator converts between units automatically to verify your setup.
How accurate are sine plate setups?
With Grade B gauge blocks (±0.000050") and a quality sine plate, you can achieve angle accuracy within a few arc-seconds. Proper wringing of gauge blocks and a clean, stable surface plate are essential for maximum accuracy.